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Mathematics

Abstract

In a regression problem the relationship between an explanatory variable X and a response variable Y may be expressed as E(Y|X = x) = m(x), where m(x) is some unknown function estimated based on random sample of pairs of observations on (X, Y). In a parametric approach m(x) is a function that can be fully described by a finite set of parameters. In practice, there are many situations where such a curve may not describe the data at all. In such a case a nonparametric approach to estimate m(x) without reference to a specific functional form may be employed. In this thesis, we adopt a nonparametric approach, known as kernel regression. Adopting results from kernel density estimation, expressions for bias, variance, and related properties of Nadaraya-Watson kernel regression estimator are derived. The confidence bands based on the estimator are also derived. The procedure is applied to a simulated data and also to two real data sets. It is shown that only a nonparametric approach is suitable in one of the real data sets. The confidence bands for the estimated smoothing curve are also provided in each situation.